His son, who left the group in 1980, posted the news on his Facebook page.
The Westboro Baptist Church gained world-wide notoriety for picketing the funerals of US servicemen killed in Iraq and Afghanistan.
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Their signs - typically saying something along the lines of 'God Hates Fags' - blamed society's acceptance of homosexuality for their deaths as well as natural disasters and other terrible events.
Documentary maker, Louis Theroux, followed the group in 2007 and documented their warped world view which they forced upon the children of member of the church.
Phelps, 84, was the patriarch of the organisation which he started in 1955, closely controlling members and ensuring his teachings were rigidly followed.